Movement error identification method for machine tool

ABSTRACT

A motion error of a machine tool in a coordinate system having its origin at an arbitrary position is identified by means of error data measured by a commonly-used method. An X-axis feed mechanism, a Y-axis feed mechanism, and a Z-axis feed mechanism are operated in a three-dimensional space of a machine coordinate system to measure translational errors, angular errors, and perpendicularity errors thereof, and error data for translational error parameters, angular error parameters, and perpendicularity error parameters in a three-dimensional space of a set coordinate system having its origin at a preset reference position X a , Y a , Z a  are derived based on the measured actual error data. Subsequently, a relative motion error between a spindle and a table in the three-dimensional space of the set coordinate system is derived based on the derived error data.

TECHNICAL FIELD

The present invention relates to a method of identifying a relativemotion error between a spindle for holding a tool and a table formounting a workpiece thereon in a machine tool configured to move thespindle and the table relative to each other in directions of threeorthogonal axes, an X-axis, a Y-axis, and a Z-axis.

BACKGROUND ART

Conventionally, positioning errors in X-axis, Y-axis, and Z-axis feedaxes (i.e., an X-axis feed mechanism, a Y-axis feed mechanism, and aZ-axis feed mechanism) and straightness in the feed axes are taken intoaccount as factors contributing to a motion error in a machine tool. Inorder to compensate for such a motion error, a numerical controller asdisclosed in Japanese Unexamined Patent Application Publication No.H8-152909 (Patent Literature 1 listed below) has been proposed.

This numerical controller, as disclosed in Patent Literature 1, includesgrid-point-compensation-vector storing means that stores thereingrid-point compensatio vectors which are measured in advance at gridpoints of a grid area defined by dividing a coordinate system at certainintervals in each coordinate-axis direction, interpolating means thatoutputs an interpolation pulse for each feed axis in accordance with amovement command, current-position recognizing means that recognizes acurrent position in each feed axis by adding the interpolation pulse,current-position-compensation-vector calculating means that calculates acurrent-position compensation vector at the current position based onthe grid-point compensation vectors, compensation-pulse outputting meansthat compares the current-position compensation vector with astart-point compensation vector at the previous current position beforeinterpolation and outputs an amount of change as a compensation pulse,and adding means that adds the compensation pulse to the interpolationpulse.

With this numerical controller, each time an interpolation pulse isoutput, a three-dimensional compensation vector at a current position iscalculated and the calculated three-dimensional compensation vector isadded as a compensation pulse to the interpolation pulse. Therefore, apositional error that is caused by a mechanical system in athree-dimensional space can be compensated for by a singleinterpolation-type error compensation function.

Note that the grid-point compensation vector at each grid point of thegrid area is obtained by measuring a positioning error of a referencepoint in a three-dimensional space occurring in controlling positioningin the feed axes with a certain interval, the reference point being setas appropriate on the axis of the spindle. Further, the measurement istypically carried out with a laser interferometer, a laser lengthmeasuring device, an auto-collimator, or the like. Furthermore, thereference point is typically set at, for example, a position at whichthe axis of the spindle intersects with a front end surface of thespindle or a position which is located forward away from the front endsurface of the spindle by a predetermined distance on the axis of thespindle; the reference point is determined as appropriate depending onthe measurement method.

Recently, a motion error (positioning error) in a three-dimensionalspace in a machine tool are considered to occur with errors intranslational motions in the feed axes, angular errors in the feed axes,and errors concerning perpendicularities between the feed axes affectingone another, as shown in FIG. 4. Therefore, an accurate motion error canbe identified by calculating these errors. Note that the definitions ofthe errors shown in FIG. 4 are as follows:

-   E_(XX) is a positioning error in the X-axis direction in the X-axis    feed mechanism;-   E_(YY) is a positioning error in the Y-axis direction in the Y-axis    feed mechanism;-   E_(ZZ) is a positioning error in the Z-axis direction in the Z-axis    feed mechanism;-   E_(YX) is a straightness error (in the Y-axis direction) in a plane    defined by the X-axis and the Y-axis in the X-axis feed mechanism;-   E_(ZX) is a straightness error (in the Z-axis direction) in a plane    defined by the X-axis and the Z-axis in the X-axis feed mechanism;-   E_(XY) is a straightness error (in the X-axis direction) in a plane    defined by the Y-axis and the X-axis in the Y-axis feed mechanism;-   E_(ZY) is a straightness error (in the Z-axis direction) in a plane    defined by the Y-axis and the Z-axis in the Y-axis feed mechanism;-   E_(XZ) is a straightness error (in the X-axis direction) in a plane    defined by the Z-axis and the X-axis in the Z-axis feed mechanism;-   E_(YZ) is a straightness error (in the Y-axis direction) in a plane    defined by the Z-axis and the Y-axis in the Z-axis feed mechanism;-   E_(AX) is an angular error around the X-axis in the X-axis feed    mechanism;-   E_(AY) is an angular error around the X-axis in the Y-axis feed    mechanism;-   E_(AZ) is an angular error around the X-axis in the Z-axis feed    mechanism;-   E_(BX) is an angular error around the Y-axis in the X-axis feed    mechanism;-   E_(BY) is an angular error around the Y-axis in the Y-axis feed    mechanism;-   E_(BZ) is an angular error around the Y-axis in the Z-axis feed    mechanism;-   E_(CX) is an angular error around the Z-axis in the X-axis feed    mechanism;-   E_(CY) is an angular error around the Z-axis in the Y-axis feed    mechanism;-   E_(CZ) is an angular error around the Z-axis in the Z-axis feed    mechanism;-   A₀Z is an angular error around the X-axis between the Z-axis feed    mechanism and an ideal Z-axis;-   B₀Z is an angular error around the Y-axis between the Z-axis feed    mechanism and the ideal Z-axis; and-   C₀Y is an angular error around the Z-axis between the Y-axis feed    mechanism and an ideal Y-axis.-   Note that other conceivable error factors are an angular error A₀Y    around the X-axis between the Y-axis feed mechanism and the ideal    Y-axis, an angular error B₀X around the Y-axis between the X-axis    feed mechanism and an ideal X-axis, and an angular error C₀X around    the Z-axis between the X-axis feed mechanism and the ideal X-axis.

As for a method for measuring these errors, a measurement method using ameasurement apparatus as shown in FIG. 5 has been proposed. Note thatthe machine tool 50 shown in FIG. 5, which is shown by way of exampleonly, is composed of a bed 51 having a workpiece placement surface(i.e., table) on the top thereof, a portal frame 52, and a saddle 53.The frame 52 is disposed such that a horizontal portion thereof ispositioned above the bed 51, and two vertical portions thereof areengaged with the sides of the bed 51 to allow the frame 52 to move as awhole in the Y-axis direction. The saddle 53 is engaged with thehorizontal portion of the frame 52 and is configured to be movable inthe X-axis direction along the horizontal portion of the frame 52.Further, a spindle 54 is held by the saddle 53 in a manner to be movablein the Z-axis direction and rotatable about an axis parallel to theZ-axis. The X-axis, the Y-axis, and the Z-axis are reference axes thatare orthogonal to one another, and feed axes corresponding to thereference axes are respectively constituted by an X-axis feed mechanism(not shown), a Y-axis feed mechanism (not shown), and a Z-axis feedmechanism (not shown).

The above-mentioned errors are measured with a laser length measuringdevice 101 disposed on the bed 51 as well as a mirror 102 attached tothe spindle 54. Specifically, first, the laser length measuring device101 is arranged at a predetermined position, for example, the positionindicated by the solid line in FIG. 5, and the mirror 102 is attached tothe spindle 54. Thereafter, positioning in the X-axis feed mechanism,positioning in the Y-axis feed mechanism, and positioning in the Z-axisfeed mechanism are controlled with a certain interval to sequentiallyposition the mirror 102 at each grid point of a three-dimensional spacethat is divided in a grid-like pattern with the certain interval, and ateach grid point, a laser beam is irradiated from the laser lengthmeasuring device 101 to the mirror 102 and a reflected light of thelaser beam is received by the laser length measuring device 101, wherebythe distance between the laser length measuring device 101 and themirror 102 is measured by the laser length measuring device 101.

Subsequently, the laser length measuring device 101 is sequentiallyarranged at three other different positions (for example, the positionsindicated by the broken lines in FIG. 5), and at each of the threedifferent positions, similarly to the initial measurement, the mirror102 is sequentially positioned at each grid point of thethree-dimensional space and, at each grid point, the distance betweenthe laser length measuring device 101 and the mirror 102 is measured bythe laser length measuring device 101. In this process, the mirror 102is arranged at a height position different from that in the initialmeasurement with respect to the laser length measuring device 101 at atleast one of the three different positions.

Based on the measurement data obtained in the above-described manner,the position of the mirror 102 at each grid point of thethree-dimensional space is calculated in accordance with the principleof triangulation. Further, based on the calculated position data andanalysis of the position data, the above-mentioned errors are obtained.

However, the measurement method using the laser length measuring device101 has a problem that the laser length measuring device 101 per se isexpensive, and further has a problem that the measurement requires longtime and is complicated and troublesome in operation because it isnecessary to sequentially arrange the laser length measurement device101 at four positions, and at each of the four positions, sequentiallyposition the mirror 102 at each grid point of the three-dimensionalspace to carry out the measurement.

At the same time, the translational motion errors in the feed axes andthe angular errors in the feed axes can be measured in accordance withan already established measurement method, as provided in JIS B 6190-2,JIS B 6336-1, and JIS B 6336-2. Further, as for the errors A₀Z, B₀Z,C₀Y, etc. regarding the perpendicularities between the X-axis, theY-axis, and the Z-axis, a measurement method using a double ball bar asdisclosed in Non-Patent Literature 1 listed below has been proposed.

Accordingly, the above-mentioned errors can be measured by means ofthese methods without depending on the above-described measurementmethod using the laser length measuring device 101 and the mirror 102.

CITATION LIST Patent Literature

Patent Literature 1: Japanese Unexamined Patent Application PublicationNo. H8-152909

NON-PATENT LITERATURE

Non-Patent Literature 1: Yoshiaki Kakino, Yukitoshi Ihara, and YoshioNakatsu: “A Study on the Motion Accuracy of NC Machine Tools (2ndReport)”, Journal of the Japan Society for Precision Engineering,52/10/1986 pp. 73-79

SUMMARY OF INVENTION Technical Problem

The above-described motion error of the spindle (specifically, thereference point) in a three-dimensional space has to be compensated foreventually. Therefore, typically, for control reasons, a motion error ina three-dimensional space of a machine coordinate system that is definedwith respect to the so-called machine zero has to be identified.

However, where the perpendicularity errors between the X-axis, theY-axis, and the Z-axis are measured with a double ball bar as mentionedabove, there is a problem that it is not possible to measure the errorswith respect to the machine zero. That is to say, in order to measurethe perpendicularity errors with respect to the machine zero with adouble ball bar, it is necessary to turn the spindle which has thedouble ball bar attached thereto about the machine zero with the lengthof the bar as a turning radius. However, the feed axes do not allowmovement in the negative direction beyond the machine zero; therefore,such a turning operation cannot be realized.

The above-mentioned errors E_(XX), E_(YY), E_(ZZ), E_(YX), E_(ZX),E_(XY), E_(ZY), E_(XZ), E_(YZ), E_(AX), E_(AY), E_(AZ), E_(BX), E_(BY),E_(BZ), E_(CX), E_(CY), and E_(CZ) are theoretically considered to beaffected by the perpendicularity errors A₀Z, B₀Z, C₀Y, etc. Therefore,it is conceivable that these errors also cannot be identified withrespect to the machine zero.

Thus, when the measurement methods provided in the JIS and the methoddisclosed in Non-Patent Literature 1 are used, the motion error in thethree-dimensional space of the machine coordinate system cannot beidentified immediately based on measurement values of the methods.However, if it is possible to identify the motion errors in thethree-dimensional space of the machine coordinate system based onmeasurement values measured by these methods, there is an advantage incost because the laser length measuring device 101 as shown in FIG. 5that is expensive is not required. Further, it is also advantageous thatit is not necessary to measure a positional error at each grid point setin the three-dimensional space of the mechanical coordinate system;therefore, the measurement can be carried out more simply than themeasurement using the laser length measuring device 101.

Further, if it is possible to identify the motion error in athree-dimensional space of a coordinate system having its origin at anarbitrary reference position based on measurement values measured by themeasurement methods provided in the JIS and the method disclosed inNon-Patent Literature 1, the degree of freedom of usage of the data isincreased, which is convenient.

The present invention has been achieved in view of the above-describedcircumstances, and an object thereof is to provide a method ofidentifying a motion error of a machine tool in a coordinate systemhaving its origin at an arbitrary position in the machine tool based onerror data measured by a conventional commonly-used measurement method.

Solution to Problem

The present invention, for solving the above-described problems, relatesto a method of identifying a relative motion error between a spindleholding a tool and a table for mounting a workpiece thereon in athree-dimensional space in a machine tool,

the machine tool including the spindle and the table and including aZ-axis feed mechanism, an X-axis feed mechanism, and a Z-axis feedmechanism respectively corresponding to a Z-axis, an X-axis, and aY-axis as reference axes, the Z-axis extending along an axis of thespindle, the X-axis and the Y-axis being orthogonal to the Z-axis andorthogonal to each other,

the machine tool being configured such that the spindle and the tableare moved relative to each other in the three-dimensional space by theX-axis feed mechanism, the Y-axis feed mechanism, and the Z-axis feedmechanism,

the method including:

operating the X-axis feed mechanism, the Y-axis feed mechanism, and theZ-axis feed mechanism in a three-dimensional space of a machinecoordinate system defined with respect to a machine zero X₀, Y₀, Z₀respectively set for the X-axis feed mechanism, the Y-axis feedmechanism, and the Z-axis feed mechanism, and measuring the followingerrors with respect to an arbitrary coordinate position in the machinecoordinate system:

-   -   a positioning error in the X-axis direction;    -   a positioning error in the Y-axis direction;    -   a positioning error in the Z-axis direction;    -   straightness errors in the X-axis, the Y-axis, and the Z-axis;    -   angular errors around the X-axis, the Y-axis, and the Z-axis in        the X-axis;    -   angular errors around the X-axis, the Y-axis, and the Z-axis in        the Y-axis;    -   angular errors around the X-axis, the Y-axis, and the Z-axis in        the Z-axis; and    -   perpendicularity errors between the X-axis, the Y-axis, and the        Z-axis;

deriving, based on the measured actual error data, the following errorsin a three-dimensional space of a set coordinate system having itsorigin at a reference position X_(a), Y_(a), Z_(a) preset in the machinecoordinate system:

-   -   a positioning error in the X-axis direction in the X-axis feed        mechanism;    -   a positioning error in the Y-axis direction in the Y-axis feed        mechanism;    -   a positioning error in the Z-axis direction in the Z-axis feed        mechanism;    -   straightness errors in the X-axis feed mechanism, the Y-axis        feed mechanism, and the Z-axis feed mechanism;    -   angular errors around the X-axis, the Y-axis, and the Z-axis in        the X-axis feed mechanism;    -   angular errors around the X-axis, the Y-axis, and the Z-axis in        the Y-axis feed mechanism;    -   angular errors around the X-axis, the Y-axis, and the Z-axis in        the Z-axis feed mechanism; and    -   perpendicularity errors between the X-axis feed mechanism, the        Y-axis feed mechanism, and the Z-axis feed mechanism; and

deriving, based on the derived error data, the relative motion errorbetween the spindle and the table in the three-dimensional space of theset coordinate system.

In the present invention, the X-axis feed mechanism, the Y-axis feedmechanism, and the Z-axis feed mechanism are operated in athree-dimensional space of a machine coordinate system defined withrespect to a machine zero X₀, Y₀, Z₀ respectively set for the X-axisfeed mechanism, the Y-axis feed mechanism, and the Z-axis feedmechanism, and a positioning error in the X-axis direction, apositioning error in the Y-axis direction, a positioning error in theZ-axis direction, straightness errors in the X-axis, the Y-axis, and theZ-axis, angular errors around the X-axis, the Y-axis, and the Z-axis inthe X-axis, angular errors around the X-axis, the Y-axis, and the Z-axisin the Y-axis, angular errors around the X-axis, the Y-axis, and theZ-axis in the Z-axis, and perpendicularity errors between the X-axis,the Y-axis, and the Z-axis are measured with respect to an arbitrarycoordinate position in the machine coordinate system.

The positioning error in the X-axis direction, the positioning error inthe Y-axis direction, the positioning error in the Z-axis direction, thestraightness errors in the X-axis, the Y-axis, and the Z-axis, theangular errors around the X-axis, the Y-axis, and the Z-axis in theX-axis, the angular errors around the X-axis, the Y-axis, and the Z-axisin the Y-axis, and the angular errors around the X-axis, the Y-axis, andthe Z-axis in the Z-axis can be measured, for example, in conformitywith the regulations of JIS B 6190-2, JIS B 6336-1, and JIS B 6336-2.The perpendicularity errors between the X-axis, the Y-axis, and theZ-axis can be measured, for example, by means of the double ball barmethod disclosed in Non-Patent Literature 1 listed above.

Based on the measured actual error data, a positioning error in theX-axis direction in the X-axis feed mechanism, a positioning error inthe Y-axis direction in the Y-axis feed mechanism, a positioning errorin the Z-axis direction in the Z-axis feed mechanism, straightnesserrors in the X-axis feed mechanism, the Y-axis feed mechanism, and theZ-axis feed mechanism, angular errors around the X-axis, the Y-axis, andthe Z-axis in the X-axis feed mechanism, angular errors around theX-axis, the Y-axis, and the Z-axis in the Y-axis feed mechanism, angularerrors around the X-axis, the Y-axis, and the Z-axis in the Z-axis feedmechanism, and perpendicularity errors between the X-axis feedmechanism, the Y-axis feed mechanism, and the Z-axis feed mechanism in athree-dimensional space of a set coordinate system having its origin ata reference position X_(a), Y_(a), Z_(a) preset in the machinecoordinate system are derived.

Subsequently, based on the derived error data, a relative motion errorbetween the spindle and the table, i.e., a positioning error of thespindle with respect to the table, in the three-dimensional space of theset coordinate system is derived.

As described above, in the present invention, error data relating to theX-axis feed mechanism, the Y-axis feed mechanism, and the Z-axis feedmechanism in the three-dimensional space of the set coordinate systemhaving its origin at the reference position X_(a), Y_(a), Z_(a) presetin the machine coordinate system is derived based on measured actualerror data that is measured by an existing commonly-used measurementmethod, and a motion error of the machine tool in the three-dimensionalspace of the set coordinate system is derived based on the derived errordata. Note that the reference position X_(a), Y_(a), Z_(a) can be set atany positon; for example, it may be set at the machine zero X₀, Y₀, Z₀.

Accordingly, with the present invention, a motion error of a machinetool in a three-dimensional space of a machine coordinate system can beidentified based on actual error data that is measured by an existingcommonly-used measurement method which does not use an expensive laserlength measuring device as mentioned above and which can be carried outmore simply in operation than a measurement using such a laser lengthmeasuring device. Accordingly, identification of the motion error can becarried out inexpensively and simply in operation.

Further, identifying the motion error in a set coordinate system, thereference position X_(a), Y_(a), Z_(a) of which is set at an arbitraryposition, can increase the degree of freedom of usage of the error data.

Note that the error data derived may relate to a spindle center positionon a front end of the spindle. With this configuration, a variableelement, such as protrusion of a measuring device, in the measurement ofthe actual errors can be canceled.

Further, the relative motion error between the spindle and the table inthe three-dimensional space of the set coordinate system may relate to atip of a tool to be attached to the spindle. Using a motion error amountobtained with this configuration enables appropriate motion errorcompensation which is consistent with actual machining using the tool.

Advantageous Effects of Invention

As described above, with the present invention, a motion error of amachine tool in a three-dimensional space of a machine coordinate systemcan be identified based on measured actual error data that is measuredby an existing commonly-used measurement method which does not use anexpensive laser length measuring device as mentioned above and which canbe carried out more simply in operation than a measurement using such alaser length measuring device. Accordingly, identification of the motionerror can be carried out inexpensively and simply in operation.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is an illustration for describing a motion error identificationmethod according to an embodiment of the present invention;

FIG. 2 is an illustration for describing the motion error identificationmethod according to the embodiment;

FIG. 3 is an illustration showing results of measurement of aperpendicularity between an X-axis feed mechanism and a Y-axis feedmechanism in an X-Y plane using a double ball bar;

FIG. 4 is an illustration showing error parameters causing a motionerror; and

FIG. 5 is an illustration for describing a conventional method foridentifying a motion error.

DESCRIPTION OF EMBODIMENTS

Hereinafter, a specific embodiment of the present invention will bedescribed with reference to the drawings.

In this embodiment, a method for identifying a motion error of ahorizontal machining center 1 as shown in FIGS. 1 and 2 is described.Note that the machining center 1 includes a bed 2 having a T-shape inplan view, a column 3 disposed on the bed 2 such that it is movable in adirection of an X-axis, a spindle head 4 held by the column 3 such thatit is movable in a direction of a Y-axis, a spindle 5 rotatablysupported by the spindle head 4, and a table 6 disposed on the bed 2such that it is movable along a Z-axis.

The column 3 is moved in the X-axis direction by an X-axis feedmechanism (not shown), the spindle head 4 is moved in the Y-axisdirection by a Y-axis feed mechanism (not shown), and the table 6 ismoved in the Z-axis direction by a Z-axis feed mechanism (not shown).Thus, the X-axis feed mechanism, the Y-axis feed mechanism, and theZ-axis feed mechanism cause the spindle 5 and the table 6 to moverelative to each other in a three-dimensional space formed by the threeorthogonal axes, i.e., the X-axis, the Y-axis, and the Z-axis.

1. Motion Error Calculation Equations

As for the thus-configured machining center 1, it is known that a motionerror (positioning error) of a front-end center position (referencepoint) of the spindle 5 in a three-dimensional space of a machinecoordinate system can be calculated by the equations below. Note that α,β, and γ are respectively command values for the X-coordinate, theY-coordinate, and the Z-coordinate, E_(X) (α, β, γ) is a positioningerror in the X-axis direction, E_(Y) (α, β, γ) is a positioning error inthe Y-axis direction, and E_(Z) (α, β, γ) is a positioning error in theZ-axis direction.E _(X)(α,βγ)=E _(XX)(α)+E _(XY)(β)+E _(XZ)(γ)−(E _(CX)(α)+E _(CZ)(γ)+C₀Y)×β  (Equation 1)E _(Y)(α,β,γ)=E _(YX)(α)+E _(YY)(β)+E _(YZ)(γ)+E _(CZ)(γ)×α  (Equation2)E _(Z)(α,β,γ)=E _(ZX)(α)+E _(ZY)(β)+E _(ZZ)(γ)+(E _(AX)(α)+E _(AZ)(γ)+A₀ Y)×β−(E _(BZ)(γ)+B ₀ X)×α  (Equation 3)

-   Note that the error parameters in the above equations are defined as    follows:-   E_(XX) is a positioning error in the X-axis direction in the X-axis    feed mechanism;-   E_(YY) is a positioning error in the Y-axis direction in the Y-axis    feed mechanism;-   E_(ZZ) is a positioning error in the Z-axis direction in the Z-axis    feed mechanism;-   E_(YX) is a straightness error (in the Y-axis direction) in an X-Y    plane in the X-axis feed mechanism;-   E_(ZX) is a straightness error (in the Z-axis direction) in an X-Z    plane in the X-axis feed mechanism;-   E_(XY)is a straightness error (in the X-axis direction) in a Y-X    plane in the Y-axis feed mechanism;-   E_(ZY) is a straightness error (in the Z-axis direction) in a Y-Z    plane in the Y-axis feed mechanism;-   E_(XZ) is a straightness error (in the X-axis direction) in a Z-X    plane in the Z-axis feed mechanism;-   E_(YZ) is a straightness error (in the Y-axis direction) in a Z-Y    plane in the Z-axis feed mechanism;-   E_(AX) is an angular error around the X-axis in the X-axis feed    mechanism;-   E_(AY) is an angular error around the X-axis in the Y-axis feed    mechanism;-   E_(AZ) is an angular error around the X-axis in the Z-axis feed    mechanism;-   E_(BX) is an angular error around the Y-axis in the X-axis feed    mechanism;-   E_(BY) is an angular error around the Y-axis in the Y-axis feed    mechanism;-   E_(BZ) is an angular error around the Y-axis in the Z-axis feed    mechanism;-   E_(CX) is an angular error around the Z-axis in the X-axis feed    mechanism;-   E_(CY) is an angular error around the Z-axis in the Y-axis feed    mechanism;-   E_(CZ) is an angular error around the Z-axis in the Z-axis feed    mechanism;-   A₀Y is an angular error around the X-axis between the Y-axis feed    mechanism and an ideal Y-axis;-   B₀X is an angular error around the Y-axis between the X-axis feed    mechanism and an ideal X-axis; and-   C₀Y is an angular error around the Z-axis between the Y-axis feed    mechanism and the ideal Y-axis.

Note that other conceivable error parameters are as follows:

-   an angular error A₀Z around the X-axis between the Z-axis feed    mechanism and an ideal Z-axis;-   an angular error B₀Z around the Y-axis between the Z-axis feed    mechanism and the ideal Z-axis; and-   an angular error C₀X around the Z-axis between the X-axis feed    mechanism and the ideal X-axis.

Further, a positioning error of a tool attached to the spindle 5 can becalculated by the equations below. Note that T_(X), T_(Y), T_(Z) are adeviation in the X-axis direction, a deviation in the Y-axis direction,and a deviation in the Z-axis direction of a tip of the tool withrespect to the front-end center position (reference point) of thespindle 5, respectively.E _(X)(α,β,γ, T _(X) , T _(Y) , T _(Z))=E _(XX)(α)+E _(XY)(β)+E_(XZ)(γ)−(E_(CX)(α)+E _(CZ)(γ)+C ₀ Y)×β+(E _(BX)(α)+E _(BY)(β)+E_(BZ)(γ))×T _(Z)−(E _(CX)(α)+E _(CY)(β)+E _(CZ)(γ))×T _(Y)   (Equation4)E _(Y)(α,β, γ, T_(X), T_(Y), T_(Z))=E _(YX)(α)+E _(YY)(β)+E _(YZ)(γ)+E_(CZ)(γ)×α+(E _(CX)(α)+E _(CY)(β)+E _(CZ)(γ))×T _(X)−(E _(AX)(α)+E_(AY)((β)+E _(AZ)(γ))×T _(Z)   (Equation 5)E _(Z)(α,β, γ, T_(X), T_(Y), T_(Z))=E _(ZX)(α)+E _(ZY)(β)+E _(ZZ)(γ)+(E_(AX)(α)+E _(AZ)(γ)+A ₀ Y)×β−(E _(BZ)(γ)+B ₀ X)×α+(E _(AX)(α)+E_(AY)(β)+E _(AZ)(γ))×T _(Y)−(E _(BX)(α)+E _(BY)(β)+E _(BZ)(γ))×T _(X)   (Equation 6)

Further, the equations below can calculate the positioning errors in aset coordinate system having its origin at a position X_(a), Y_(a),Z_(a) that is an arbitrary position in the machine coordinate system.E _(X)(α,β,γ)=E _(XX)(α)+E _(XY)(β)+E _(XZ)(γ)−(E _(CX)(α)+E _(CZ)(γ)+C₀ Y)×(β−Y _(a))   (Equation 7)E _(Y)(α,β,γ)=E _(YX)(α)+E _(YY)(β)+E _(YZ)(γ)+(E _(CZ)(γ)×(α−X _(a))  (Equation 8)E _(Z)(α,β,γ)=E _(ZX)(α)+E _(ZY)(β)+E _(ZZ)(γ)+(E _(AX)(α)+E _(AZ)(γ)+A₀ Y)×(β−Y _(a))−(E _(BZ)(γ)+B ₀ X)×(α−X _(a))   (Equation 9)E _(X)(α,β, γ, T_(X), T_(Y), T_(Z))=E _(XX)(α)+E _(XY)(β)+E _(XZ)(γ)−(E_(CX)(α)+E _(CZ)(γ)+C ₀ Y)×(β−Y _(a))+(E _(BX)(α)+E _(BY)(β)+E _(BZ)(γ))×T _(Z)−(E _(CX)(α)+E _(CY)(β)+E_(CZ)(γ))×T _(Y)   (Equation 10)E _(Y)(α,β, γ, T_(X), T_(Y), T_(Z))=E _(YX)(α)+E _(YY)(β)+E _(YZ)(γ)+E_(CZ)(γ)×(α−X _(a))+(E _(CX)(α)+E _(CY)(β)+E _(CZ)(γ))×T _(X)−(E _(AX)(α)+E _(AY)(β)+E_(AZ)(γ))×T _(Z)   (Equation 11)E _(Z)(α,β,γ, T_(X), T_(Y), T_(Z))=E _(ZX)(α)+E _(ZY)(β)+E _(ZZ)(γ)+(E_(AX)(α)+E _(AZ)(γ)+A ₀ Y)×(β−Y _(a))−(E _(BZ)(γ)+B ₀ X)×(α−X _(a))+(E_(AX)(α)+E _(AY)(β)+E _(AZ)(γ))×T _(Y)−(E _(BX)(α)+E _(BY)(β)+E_(BZ)(γ))×T _(X)   (Equation 12)

2. Motion Error Measurement

In this embodiment, firstly, errors are measured for the items below inconformity with JIS B 6190-2 and JIS B 6336-1. Note that, in thedescription below, X, Y, and Z representing a position represent theposition of the front-end center (reference point) of the spindle 5 inthe machine coordinate system, X, Y, and Z representing the position ofthe reference point with respect to a machine zero in the X-axis feedmechanism, the Y-axis feed mechanism, and the Z-axis feed mechanism,respectively.

[X-Axis]

The X-axis feed mechanism (not shown) is actuated and the referencepoint is sequentially moved to command positions X₁, X₂, . . . and X_(n)at predetermined pitch intervals, during which errors M^(I1) (X_(k))through M^(I6)(X_(k)) for the measurement items 11 through I₆ below aremeasured. Note that k is an integer from 1 to n. Note further thatcommand positions in the Y-axis feed mechanism (not shown) and Z-axisfeed mechanism (not shown) during measurement of each measurement itemare respectively arbitrary positions Y^(Im) and Z^(Im), m correspondingto the suffix of the measurement item.

-   I₁: an X-axis positioning error M^(I1)(X_(k)) is measured (JIS B    6190-2)-   I₂: an X-axis straightness error M^(I2)(X_(k)) is measured (in the    Y-axis direction) (JIS B 6336-1)-   I₃: an X-axis straightness error M^(I3)(X_(k)) is measured (in the    Z-axis direction) (JIS B 6336-1)-   I₄: an X-axis angular error M^(I4)(X_(k)) is measured (around the    X-axis) (JIS B 6336-1)-   I₅: an X-axis angular error M^(I5)(X_(k)) is measured (around the    Y-axis) (JIS B 6336-1)-   I₆: an X-axis angular error M^(I6)(X_(k)) is measured (around the    Z-axis) (JIS B 6336-1)

[Y-Axis]

The Y-axis feed mechanism (not shown) is actuated and the referencepoint is subsequently moved to command positions Y₁, Y₂, . . . and Y_(n)at predetermined pitch intervals, during which errors M^(I7)(Y _(k))through M^(I12)(Y _(k)) for the measurement items I₇ through I₁₂ beloware measured. Note that k is an integer from 1 to n. Note further thatcommand positions in the X-axis feed mechanism (not shown) and theZ-axis feed mechanism (not shown) during measurement of each measurementitem are respectively arbitrary positions X^(Im) and Z^(Im), mcorresponding to the suffix of the measurement item.

-   I₇: a Y-axis positioning error M^(I7)(Y _(k)) is measured (JIS B    6190-2)-   I₈: a Y-axis straightness error M^(I8)(Y _(k)) is measured (in the    X-axis direction) (JIS B 6336-1)-   I₉: a Y-axis straightness error M^(I9)(Y _(k)) is measured (in the    Z-axis direction) (JIS B 6336-1)-   I₁₀: a Y-axis angular error M^(I10)(Y _(k)) is measured (around the    X-axis) (JIS B 6336-1)-   I₁₁: a Y-axis angular error M^(I11)(Y _(k)) is measured (around the    Y-axis) (JIS B 6336-1)-   I₁₂: a Y-axis angular error M^(I12)(Y _(k)) is measured (around the    Z-axis) (JIS B 6336-1)

[Z-Axis]

The Z-axis feed mechanism (not shown) is actuated and the referencepoint is sequentially moved to command positions Z₁, Z₂, . . . and Z_(n)at predetermined pitch intervals, during which errors M^(I13)(Z _(k))through M^(I18)(Z _(k)) for the measurement items 113 through I₁₈ beloware measured. Note that k is an integer from 1 to n. Note further thatcommand positions in the X-axis feed mechanism (not shown) and theY-axis feed mechanism (not shown) during measurement of each measurementitem are respectively arbitrary positions X^(Im) and Y^(Im), mcorresponding to the suffix of the measurement item.

-   I₁₃: a Z-axis positioning error M^(I13)(Z _(k)) is measured (JIS B    6190-2);-   I₁₄: a Z-axis straightness error M^(I14)(Z _(k)) is measured (in the    X-axis direction) (JIS B 6336-1);-   I₁₅: a Z-axis straightness error M^(I15)(Z _(k)) is measured (in the    Y-axis direction) (JIS B 6336-1);-   I₁₆: a Z-axis angular error M^(I16)(Z _(k)) is measured (around the    X-axis) (JIS B 6336-1);-   I₁₇: a Z-axis angular error M^(I17)(Z _(k)) is measured (around the    Y-axis) (JIS B 6336-1); and-   I₁₈: a Z-axis angular error M^(I18)(Z _(k)) is measured (around the    Z-axis) (JIS B 6336-1).

[Perpendicularity]

Measurement is performed with a double ball bar In accordance withNon-Patent Literature 1, wherein the center position of the table-sideball is set at an arbitrary position X_(i), Y_(i), Z_(i) , the referencepoint of the spindle 5 is circularly moved with the length of the bar asa rotation radius in an X-Y plane, in an X-Z plane, and in a Y-Z plane,and lengths M_(Aij) (in the Y-Z plane), M_(Bij) (in the X-Z plane), andM_(Cij) (in the X-Y plane) of the bar are measured based on the amountof expansion/contraction of the bar. M_(Aij) is a length of the bar at aposition Y_(Aij), Z_(Aij) in the circular movement of the referencepoint of the spindle 5 in the Y-Z plane that is defined with X_(i)fixed, M_(Bij) is a length of the bar at a position X_(Bij), Z_(Bij) inthe circular movement of the reference point of the spindle 5 in the X-Zplane that is defined with Y_(i) fixed, and M_(Cij) is a length of thebar at a position X_(Cij), Y_(Cij) in the circular movement of thereference point of the spindle 5 in the X-Y plane that is defined withZ_(i) fixed. Note that i is an integer from 1 to g and means the numberof times of perpendicularity measurement, and j is an integer from 1 toh and means a sampling number of the position of the spindle 5.

FIG. 3 shows an example of measurement data (amount ofexpansion/contraction of the bar) obtained by measuring theperpendicularity between the X-axis feed mechanism and the Y-axis feedmechanism in the X-Y plane with a double ball bar. In FIG. 3, one of thetwo solid line depictions represents measurement data for normalrotation of the reference point of the spindle 5, and the otherrepresents measurement data for reverse rotation of the reference pointof the spindle 5. Further, the bold dotted-and-dashed line circlerepresents a reference circle and the thin dotted-and-dashed linecircles represent graduations.

Based on the obtained measurement values M_(Aij), M_(Bij) and M_(Cij),perpendicularities P_(Ai), P_(Bi), and P_(Ci) and perpendicularityerrors A₀Y_(i), B₀X_(i), and C₀Y_(i) for the X-axis feed mechanism, theY-axis feed mechanism, and the Z-axis feed mechanism when the centerposition of the table-side ball is positioned at theposition X_(i),Y_(i), Z_(i) are calculated in accordance with Non-Patent Literature 1.

-   Note that:-   P_(Ai) is a perpendicularity between the Y-axis feed mechanism and    the ideal Z-axis;-   P_(Bi) is a perpendicularity between the X-axis feed mechanism and    the ideal Z-axis;-   P_(Ci) is a perpendicularity between the Y-axis feed mechanism and    the ideal X-axis;-   A₀Y_(i) is an angular error around the X-axis between the Y-axis    feed mechanism and the ideal Y-axis;-   B₀X_(i) is an angular error around the Y-axis between the X-axis    feed mechanism and the ideal X-axis; and-   C₀Y_(i) is an angular error around the Z-axis between the Y-axis    feed mechanism and the ideal Y-axis.

Note that the perpendicularities P_(Ai), P_(Bi), and P_(Ci) arerespectively represented as functions of the measurement values M_(Aij),M_(Bij), and Mg as follows:

-   f_(A)(M_(Ai))=P_(Ai);-   f_(B)(M_(Bi))=P_(Bi); and-   f_(C)(M_(Ci))=P_(Ci),-   where M_(Ai) is total data of the measurement value M_(Aij) from j=1    through j=h, M_(Bi) is total data of the measurement value M_(Bij)    from j=1 through j=h, and M_(Ci) is total data of the measurement    value M_(Cij) from j=1 through j=h.

3. Identification of Error Parameters the X-Axis Feed Mechanism, Y-ZxisFeed Mechanism, and Z-Axis Feed Mechanism

Subsequently, the above-mentioned error parameters E_(XX), E_(YY),E_(ZZ), E_(YX), E_(ZX), E_(XY), E_(ZY), E_(XZ), E_(YZ), E_(AX), E_(AY),E_(AZ), E_(BX), E_(BY), E_(BZ), E_(CX), E_(CY), and E_(CZ) in the X-axisfeed mechanism, the Y-axis feed mechanism, and the Z-axis feed mechanismare identified based on the error data M^(I1)(X_(k)) throughM^(I6)(X_(k)), M^(I7)(Y _(k)) through M^(I12)(Y _(k)), and M^(I13)(Z_(k)) through M^(I18)(Z _(k)) measured in the above-described manner.

By way of example, the X-axis straightness error M^(I3)(X_(k)) (in theZ-axis direction) is examined. As shown in FIGS. 1 and 2, thestraightness error M^(I3)(X_(k)) is measured with an indicator (e.g., adial gauge) protruding from the command positions in the X-axis, theY-axis, and the Z-axis; therefore, the protrusion is regarded as anerror factor. Since the command values Y^(I3) and Z^(I3) in the Y-axisand the Z-axis, which are other than the X-axis as the measurementtarget, as well as protrusion amounts L^(I3) _(x)L^(I3) _(Y), and L^(I3)_(Z) of the indicator in the three directions are fixed, thestraightness error M^(I3)(X_(k)) can be represented by the followingequation:M ^(I3)(X _(k))=E _(Z)(X_(k) , Y ^(I3) ,Z ^(I3) ,L ^(I3) _(X) ,L ^(I3)_(Y) ,L ^(I3) _(Z))+Const^(I3).

-   Note that Const^(I3) is a constant term.

When E_(Z)(X_(k), Y^(I3),Z^(I3),L_(X),L_(Y),L_(Z)) in the above equationis expanded as an error in the set coordinate system having its originat the position X_(a), Y_(a), Z_(a) that is an arbitrary position in themachine coordinate system, the equation below is obtained according toEquation 12.M ^(I3)(X _(k))=E _(ZX)(X _(k))+E _(ZY)(Y ^(I3))+E _(ZZ)(Z ^(I3))+(E_(AX)(X _(k))+E _(AZ)(Z ^(I3))+A ₀ Y)×(Y ^(I3) −Y _(a))−(E _(BZ)(Z^(I3))+B ₀ X)×(X _(k) −X _(a))+(E _(AX)(X _(k))+E _(AY)(Y ^(I3))+E_(AZ)(Z ^(I3)))×L ^(I3) _(Y)−(E_(BX)(X _(k))+E _(BY)(Y ^(I3))+E _(BZ)(Z^(I3)))×L ^(I3)×+Const^(I3)

-   Further, when the constant terms are consolidated into Const^(I3),    the equation below is obtained.    M ^(I3)(X _(k))=E _(ZX)(X _(k))+E _(AX)(X _(k))×(Y ^(I3) −Y _(a))+(E    _(BZ)(Z ^(I3))+B ₀ X)×X _(k) +E _(AX)(X _(k))×L ^(I3) _(Y) −E    _(BX)(X _(k))×L ^(I3) _(X)+Const^(I3)-   Furthermore, when E′_(ZX)(X _(k))=E _(ZX)(X _(k))+(E _(BZ)(Z    ^(I3))+B ₀ X)×X _(k) is intoruced, the equation below is obtained.    M ^(I3)(X _(k))=E′ _(ZX)(X _(k))+E _(AX)(X _(k))×(Y ^(I3) −Y    _(a))+E_(AX)(X _(k))×L ^(I3) _(Y) −E _(BX)(X _(k))×L ^(I3)    _(X)+Const^(I3)-   Since E′_(ZX)(X_(k)) can be considered to be equivalent to    E_(ZX)(X_(k)), the equation below is obtained eventually.    M ^(I3)(X _(k))=E _(ZX)(X _(k))+E _(AX)(X _(k))×(Y ^(I3) −Y    _(a))+E_(AX)(X _(k))×L ^(I3) _(Y) −E _(BX)(X _(k))×L ^(I3)    _(X)+Const^(I3)-   Thus, the X-axis straightness error M^(I3)(X_(k)) can be represented    by an equation which does not use the perpendicularity (B₀X) in the    X-axis feed mechanism and the perpendicularity (A₀Y) in the Y-axis    feed mechanism.

Further, the X-axis angular error M^(I6)(X_(k)) around the Z-axis isexamined. Since the angular errors involve no other error factors, theangular error M_(I6)(X_(k)) can be represented by the followingequation:

M^(I6)(X _(k))=E _(CX)(X _(k))+Const^(I6).

-   Note that Const^(I6) is a constant term.

On the basis of the above examination, the above-mentioned errors can berepresented by equations which do not use the perpendicularity (B₀X) inthe X-axis feed mechanism, the perpendicularity (A₀Y) in the Y-axis feedmechanism, and the perpendicularity (C₀Y) in the Z-axis feed mechanismas follows:M ^(I1)(X _(k))=E _(XX)(X _(k))−E _(CX)(X _(k))×(Y ^(I1) −Y _(a))+E_(BX)(X _(k))×L ^(I1) _(Z) −E _(CX)(X _(k))×L ^(I1) _(Y)+Const^(I1);M ^(I2)(X _(k))=E _(YX)(X _(k))+E _(CX)(X _(k))×L ^(I2) _(X) −E _(AX)(X_(k))>L ^(I2) _(Z)+Const^(I2);M ^(I3)(X _(k))=E _(ZX)(X _(k))+E _(AX)(X _(k))×(Y ^(I3) −Y _(a))+E_(AX)(X _(k))×L ^(I3) _(Y) −E _(BX)(X _(k))×L ^(I3) _(X)+Const^(I3);M ^(I4)(X _(k))=E _(AX)(X _(k))+Const^(I4);M ^(I5)(X _(k))=E _(BX)(X _(k))+Const^(I5);M ^(I6)(X _(k))=E _(CX)(X _(k))+Const^(I6);M ^(I7)(Y _(k))=E _(YY)(Y _(k))+E _(CY)(Y _(k))×L ^(I7) _(X) −E _(AY)(Y_(k))×L ^(I7) _(Z)+Const^(I7);M ^(I8)(Y _(k))=E _(XY)(Y _(k))+E _(BY)(Y _(k))×L ^(I8) _(X) −E _(AY)(Y_(k))×L ^(I8) _(Z)+Const^(I8);M ^(I9)(Y _(k))=E _(ZY)(Y _(k))+E _(AY)(Y _(k))×L ^(I9) _(X) −E _(AY)(Y_(k))×L ^(I9) _(Z)+Const^(I9);M ^(I10)(Y _(k))=E _(AY)(Y _(k))+Const^(I10);M ^(I11)(Y _(k))=E _(BY)(Y _(k))+Const^(I11);M ^(I12)(Y _(k))=E _(CY)(Y _(k))+Const^(I12);M ^(I13)(Z _(k))=E _(ZZ)(Z _(k))+E _(AZ)(Z _(k))×(Y ^(I13) −Y _(a))−E_(BZ)(Z _(k))×(X ^(I13) −X _(a))^(I) +E _(AZ)(Z _(k))×L ^(I13) _(Y) −E_(BZ)(Z _(k))×L ^(I3) _(X)+Const^(I3);M ^(I14)(Z _(k))=E _(XZ)(Z _(k))−E _(CZ)(Z _(k))×(Y ^(I14) −Y _(a))+E_(BZ)(Z _(k))×L ^(I14) _(Z) −E _(CZ)(Z _(k))×L ^(I14) _(Y)+Const^(I2),M ^(I15)(Z _(k))=E _(YZ)(Z _(k))+E _(CZ)(Z _(k))×(X ^(I13) −X _(a))+E_(CZ)(Z _(k))×L ^(I15) _(X) −E _(AZ)(Z _(k))×L ^(I15) _(Z)+Const^(I15),M ^(I16)(Z _(k))=E _(AZ)(Z _(k))+Const^(I16);M ^(I17)(Z _(k))=E _(BY)(Z _(k))+Const^(I17); andM ^(I18)(Z _(k))=E _(CY)(Z _(k))+Const^(I18).

Based on these equations, the error parameters are as follows:E _(XX)(X _(k))=M ^(I1)(X _(k))+E _(CX)(X _(k))×(Y ^(I1) −Y _(a))−E_(BX)(X _(k))×L ^(I1) _(Z) +E _(CX)(X _(k))×L ^(I1) _(Y)−Const^(I1);E _(YX)(X _(k))=M ^(I2)(X _(k))−E _(CX)(X _(k))×L ^(I2) _(X) +E _(AX)(X_(k))×L ^(I2) _(Z)−Const^(I2);E _(ZX)(X _(k))=M ^(I3)(X _(k))−E _(AX)(X _(k))×(Y ^(I3) −Y _(a))−E_(AX)(X _(k))×L ^(I3) _(Y) +E _(BX)(X _(k))×L ^(I3) _(X)−Const^(I3);E _(AX)(X _(k))=M ^(I4)(X _(k))−Const^(I4);E _(BX)(X _(k))=M ^(I5)(X _(k))−Const^(I5);E _(CX)(X _(k))=M ^(I6)(X _(k))−Const^(I6);E _(YY)(Y _(k))=M ^(I7)(Y _(k))−E _(CY)(Y _(k))×L ^(I7) _(X) +E _(AY)(Y_(k))×L ^(I7) _(Z)+Const^(I7);E _(XY)(Y _(k))=M ^(I8)(Y _(k))−E _(BY)(Y _(k))×L ^(I8) _(X) +E _(CY)(Y_(k))×L ^(I8) _(Y)+Const^(I8);E _(ZY)(Y _(k))=M ^(I9)(Y _(k))−E _(AY)(Y _(k))×L ^(I9) _(Y) +E _(BY)(Y_(k))×L ^(I9) _(X)+Const^(I9);E _(AY)(Y _(k))=M ^(I10)(Y _(k))−Const^(I10);E _(BY)(Y _(k))=M ^(I11)(Y _(k))−Const^(I11);E _(CY)(Y _(k))=M ^(I12)(Y _(k))−Const^(I12);E _(ZZ)(Z _(k))=M ^(I13)(Z _(k))−E _(AZ)(Z _(k))×(Y ^(I13) −Y _(a))+E_(BZ)(Z _(k))×(X ^(I13) −X _(a))^(I) −E _(AZ)(Z _(k))×L ^(I13) _(Y) +E_(BZ)(Z _(k))×L ^(I13) _(X)−Const^(I13);E _(XZ)(Z _(k))=M ^(I14)(Z _(k))+E _(CZ)(Z _(k))×(Y ^(I14) −Y _(a))−E_(BZ)(Z _(k))×L ^(I14) _(Z) +E _(CZ)(Z _(k))×L ^(I14) _(Y)−Const^(I2);E _(YZ)(Z _(k))=M ^(I15)(Z _(k))−E _(CZ)(Z _(k))×(X ^(I15) −X _(a))−E_(CZ)(Z _(k))×L ^(I15) _(X) +E _(AZ)(Z _(k))×L ^(I15) _(Z)−Const^(I15);E _(AZ)(Z _(k))=M ^(I16)(Z _(k))−Const^(I16);E _(BY)(Z _(k))=M ^(I17)(Z _(k))−Const^(I17); andE _(CY)(Z _(k))=M ^(I18)(Z _(k))−Const^(I18).

Thus, the error parameters in the set coordinate system having itsorigin at the position X_(a), Y_(a), Z_(a) that is an arbitrary positionin the machine coordinate system can be identified by the aboveequations. Note that the constant terms Const^(I1) through Const^(I18)can be each considered as the degree of freedom for changing setting ofthe zero point for the respective error.

4. Identification of Perpendicularity Error Parameters

Subsequently, based on the perpendicularity measurement values M_(Aij),M_(Bij), and M_(Cij) measured in the above-described manner, theperpendicularities P_(Ai), P_(Bi), and P_(Ci) which are calculatedbelow, and the perpendicularity errors A₀Y_(i), B₀X_(i), and C₀Y_(i),the perpendicularity errors A₀Y, B₀X, and C₀Y in the set coordinatesystem having its origin at the position X_(a), Y_(a), Z_(a) that is anarbitrary position in the machine coordinate system are identified.

Prior to identification of the perpendicularity errors A₀Y, B₀X, andC₀Y, the calculation basis for the identification is described. Asdescribed above, the perpendicularities P_(Ai), P_(Bi), and P_(Ci) arerespectively represented as functions of the measurement values M_(Aij),M_(Bij), and M_(Cij) as follows:f _(A)(R _(Aij))=P _(Ai);   (Equation 13)f _(B)(R _(Bij))=P _(Bi); and   (Equation 14)f _(C)(R _(Cij))=P _(Ci),   (Equation 15)where M_(Ai) is total data of the measurement value M_(Aij), M_(Bij) istotal data of the measurement value M_(Bij), and M_(Ci) is total data ofthe measurement value M_(Cij).

On the other hand, when the spindle 5 is circularly moved with a doubleball bar, the positioning errors of the spindle 5 with respect to thecommand values in the set coordinate system having its origin at theposition X_(a), Y_(a), Z_(a) that is an arbitrary position in themachine coordinate system can be calculated by Equations 10 to 12 above.Therefore, where the position of the table-side sphere in the machinecoordinate system is represented by X_(i), Y_(i), Z_(i) and the positionof the reference point of the spindle 5 circularly moved in the X-Yplane with respect to the position X_(i), Y_(i), Z_(i) is represented byX_(ik), Y_(ik), Z_(i) , the length S_(Cik) of the bar can be calculatedby the following equation:S _(Cik)=((X _(ik) +E _(Xik) −X _(i))²+(Y _(ik) +E _(Yik) −Y _(i))²+(Z_(i) +E _(Zik) −Z _(i))²)^(1/2).   (Equation 16)

-   Note that E_(Xik), E_(Yik), and E_(Zik) are the positioning errors    of the spindle 5 calculated by Equations 10 to 12 above. The    calculation of the positioning errors of the spindle 5 is carried    out with C₀Y in Equation 10 and A₀Y and B₀X in Equation 12 being    respectively replaced by arbitrary values C₀Y′, A₀Y′ and B₀X′ that    are temporary values.-   E_(Xik)=E_(X)(X_(ik), Y_(ik), Z_(i) ,t_(X),t_(Y),t_(Z))-   E_(Yik)=E_(Y)(X_(ik), Y_(ik), Z_(i) ,t_(X),t_(Y),t_(Z))-   E_(Zik)=E_(Z)(X_(ik), Y_(ik), Z_(i) ,t_(X),t_(Y),t_(Z))-   Note that t_(X), t_(Y), and t_(Z) are distances of deviation of the    spindle-side sphere from the reference point of the spindle 5 in the    X-axis direction, the Y-axis direction, and the Z-axis direction,    respectively.

In Equation 16 above, E_(Xik), E_(Yik), and E_(Zik) are infinitesimalvalues; therefore, where the squared terms thereof are approximated byzero, S_(cik) can be represented by the following equation:S _(Cik)=((X _(ik) −X _(i))²+(Y _(ik) −Y _(i))²+2E _(Xik)(X _(ik) −X_(i))+2E _(Yik)(Y _(ik) −Y _(i)))^(1/2).   (Equation 17)

Further, where total data of the length S_(Cik) of the bar calculated isrepresented by S_(Ci), a perpendicularity P′_(Ci) calculated from S_(Ci)can be represented by the following relational equation:f(S _(Ci))=P′ _(Ci).   (Equation 18)

-   Here, if the temporary perpendicularity error C₀Y′ is equal to the    true perpendicularity error C₀Y in the set coordinate system having    its origin at the position X_(a), Y_(a), Z_(a) that is an arbitrary    position in the machine coordinate system, the following relational    equation holds:    C ₀ Y−P _(Ci) =C ₀ Y′−P′ _(Ci).-   When this equation is transformed, the equation below is obtained.    C ₀ Y=C ₀ Y′−P′ _(Ci) P _(Ci).   (Equation 19)

Accordingly, by using Equation 19 above, the true perpendicularity errorC₀Y in the set coordinate system having its origin at the positionX_(a), Y_(a), Z_(a) that is an arbitrary position in the machinecoordinate system can be identified based on the temporaryperpendicularity error C₀Y′, the perpendicularity P_(Ci) calculated byEquation 15, and the perpendicularity P′_(Ci) calculated by Equation 18.

Similarly, as for the perpendicularity error B₀X, where the referencepoint of the spindle 5 circularly moved in the X-Z plane is representedby X_(ik), Y_(i), Z_(ik), the length S_(Bik) of the bar is as follows:S _(Bik)=((X _(ik) +E _(Xik) −X _(i))²+(Y _(i) +E _(Yik) −Y _(i))²+(Z_(ik) +E _(Zik) −Z _(i))²)^(1/2).

-   Where the squared terms of E_(Xik), E_(Yik), and E_(Zik) that are    infinitesimal values are approximated by zero, S_(Bik) is as    follows:    S _(Bik)=((X _(ik) −X _(i))²+(Z _(ik) −Z _(i))²+2E _(Xik)(X _(ik) −X    _(i))+2E _(Zik)(Z _(ik) −Z _(i)))^(1/2).   (Equation 20)-   Where total data of the length S_(Bik) of the bar calculated is    represented by S_(Bi), a perpendicularity P′_(Bi) calculated from    S_(Bi) can be represented by the following relational equation:    f(S _(Bi))=P′ _(Bi).   (Equation 21)

Accordingly, the true perpendicularity error B₀X in the coordinatesystem having it origin at the position X_(a), Y_(a), Z_(a) that is anarbitrary position in the machine coordinate system can be identified byEquation 22 below based on the temporary perpendicularity error B₀X′,the perpendicularity P_(Bi) calculated by Equation 14 above, and theperpendicularity P′_(Bi) calculated by Equation 21 above.B ₀ X=B ₀ X′−P′ _(Bi) +P _(Bi)   (Equation 22)

Further, as for the perpendicularity error A₀Y, where the position ofthe spindle 5 circularly moved in the Y-Z plane is represented by X_(i),Y_(ik), Z_(ik), the length S_(Aik) of the bar is as follows:S _(Aik)=((X _(i) +E _(Xik) −X _(i))²+(Y _(ik) +E _(Yik) −Y _(i))²+(Z_(ik) +E _(Zik) −Z _(i))²)^(1/2).

-   Where the squared terms of E_(Xik), E_(Yik), and E_(Zik) that are    infinitesimal values are approximated by zero, S_(Aik) is as    follows:    S _(Aik)=((Y _(ik) −Y _(i))²+(Z _(ik) −Z _(i))²+2E _(Yik)(Y _(ik) −Y    _(i))+2E _(Zik)(Z _(ik) −Z _(i)))^(1/2).   (Equation 23)

Where total data of the length S_(Aik) of the bar calculated isrepresented by S_(Ai), a perpendicularity P′_(Ai) calculated from S_(Ai)can be represented by the following relational equation:f(S _(Ai))=P′ _(Ai).   (Equation 24)

Accordingly, the true perpendicularity error A₀Y in the coordinatesystem having it origin at the position X_(a), Y_(a), Z_(a) that is anarbitrary position in the machine coordinate system can be identified byEquation 25 below based on the temporary perpendicularity error A₀Y′,the perpendicularity P_(Ai) calculated by Equation 13 above, and theperpendicularity P′_(Ai) calculated by Equation 24 above.A ₀ Y=A ₀ Y′−P′ _(Ai) +P _(Ai).   (Equation 25)

In the above-described manner, the perpendicularly errors A₀Y, B₀X, andC₀Y in the set coordinate system having its origin at the positionX_(a), Y_(a), Z_(a) that is an arbitrary position in the machinecoordinate system are identified. Note that, in the case where theperpendicularity errors A₀Y, B₀X, and C₀Y in the machine coordinatesystem defined with respect to the machine zero are identified, theperpendicularity errors A₀Y, B₀X, and C₀Y are identified with values ofE_(Xik), E_(Yik), and E_(Zik) which are calculated under the conditions:X_(a)=0, Y_(a)=0, and Z_(a)=0.

5. Identification of Motion Error

Based on the error parameters identified in the above-described manners,the positioning errors E_(X)(α,β,γ), E_(Y)(α, β, γ), and E_(Z)(α,β,γ) ofthe reference point of the spindle 5 in the three-dimensional space ofthe machine coordinate system are identified by Equations 1 to 3 above,and the positioning errors E_(X)(α,β,γ, T_(X), T_(Y), T_(Z)),E_(Y)(α,β,γ, T_(X), T_(Y), T_(Z)), and E_(Z)(α,β,γ, T_(X), T_(Y), T_(Z))of the tip of the tool attached to the spindle 5 in thethree-dimensional space of the machine coordinate system are identifiedby Equations 4 to 6 above.

Further, the positioning errors E_(X)(α,β,γ), E_(Y)(α, β, γ), andE_(Z)(α,β,γ) of the reference point of the spindle 5 in the setcoordinate system having its origin at the poaition X_(a), Y_(a), Z_(a)that is an arbitrary position in the machine coordinate system areidentified by Equations 7 to 9 above, and the positioning errorsE_(X)(α,β,γ, T_(X), T_(Y), T_(Z)), E_(Y)(α,β,γ, T_(X), T_(Y), T_(Z)),and E_(Z)(α,β,γ, T_(X), T_(Y), T_(Z)) of the tip of the tool attached tothe spindle 5 in the set coordinate system having its origin at theposition X_(a), Y_(a), Z_(a) that is an arbitrary position in themachine coordinate system are identified by Equations 10 to 12 above.

Thus, in this embodiment, the motion error (positioning errors) E_(X)(α,β, γ), E_(Y)(α, β, γ), E_(Z)(α, β, γ) of the reference point of thespindle 5 and the positioning errors E_(X)(α,β,γ, T_(X), T_(Y), T_(Z)),E_(Y)(α,β,γ, T_(X), T_(Y), T_(Z)), and E_(Z)(α,β,γ, T_(X), T_(Y), T_(Z))of the tool tip in the set coordinate system having its origin at theposition X_(a), Y_(a), Z_(a) that is an arbitrary position in themachine coordinate system can be calculated in the above-describedmanner. Further, the motion error E_(X)(α,β,γ), E_(Y)(α, β, γ),E_(Z)(α,β,γ) and errors E_(X)(α,β, γ, T_(X), T_(Y), T_(Z)), E_(Y)(α,β,γ,T_(X), T_(Y), T_(Z)), and E_(Z)(α,β,γ, T_(X), T_(Y), T_(Z)) in themachine coordinate system can be calculated by using the conditions:X_(a)=0, Y_(a)=0, and Z_(a)=0.

As described above, in this embodiment, the motion errors of thereference point and the motion errors of the tool tip in thethree-dimensional space of the machine coordinate system and in thethree-dimensional space of the set coordinate system having its originat the arbitrary reference position X_(a), Y_(a), Z_(a) can beidentified based on actual error data that is measured by means of thecommonly-used measurement methods complying with the regulations of JIS.Therefore, identification of the motion errors can be carried outinexpensively and simply in operation.

Further, since the motion errors in the set coordinate system having itsorigin at the arbitrary reference position X_(a), Y_(a), Z_(a) can beidentified, the degree of freedom of usage of the error data isincreased.

Hereinbefore, one embodiment of the present invention has beendescribed. However, the present invention is not limited thereto and canbe implemented in other modes.

For example, the measurement of the errors in the above embodimentcomplies with the regulations of JIS; however, the errors may bemeasured by means of any other method which is able to measure theerrors as accurately and easily as or more accurately and easily thanthe regulations of JIS.

The equations above for calculating the error parameters E_(XX), E_(YY),E_(ZZ), E_(YX), E_(ZX), E_(XY), E_(ZY), E_(XZ), E_(YZ), E_(AX), E_(AY),E_(AZ), E_(BX), E_(BY), E_(BZ), E_(CX), E_(CY), and E_(CZ) are shown byway of example only; the present invention is not limited thereto andthese error parameters may be calculated by other equations. Theidentification of the perpendicularity errors A₀Y, B₀X, and C₀Y is notlimited to the above example as well, and these perpendicularity errorsmay be identified by means of any other method.

REFERENCE SIGNS LIST

1 Machine tool

2 Bed

3 Colum

4 Spindle head

5 Spindle

6 Table

The invention claimed is:
 1. A method of identifying a relative motionerror between a spindle for holding a tool and a table for mounting aworkpiece thereon in a three-dimensional space in a machine tool, themachine tool including the spindle and the table and including a Z-axisfeed mechanism, an X-axis feed mechanism, and a Y-axis feed mechanismrespectively corresponding to a Z-axis, an X-axis, and a Y-axis asreference axes, the Z-axis extending along an axis of the spindle, theX-axis and the Y-axis being orthogonal to the Z-axis and orthogonal toeach other, the machine tool being configured such that the spindle andthe table are moved relative to each other in the three-dimensionalspace by the X-axis feed mechanism, the Y-axis feed mechanism, and theZ-axis feed mechanism, the method comprising: operating the X-axis feedmechanism, the Y-axis feed mechanism, and the Z-axis feed mechanism in athree-dimensional space of the machine tool coordinate system definedwith respect to the machine tool at zero position X₀, Y₀, Z₀respectively set for the X-axis feed mechanism, the Y-axis feedmechanism, and the Z-axis feed mechanism, and measuring following errorswith respect to an arbitrary coordinate position in the machine toolcoordinate system: a positioning error in the X-axis direction; apositioning error in the Y-axis direction; a positioning error in theZ-axis direction; translational errors in the X-axis, the Y-axis, andthe Z-axis; angular errors around the X-axis, the Y-axis, and the Z-axisin the X-axis; angular errors around the X-axis, the Y-axis, and theZ-axis in the Y-axis; angular errors around the X-axis, the Y-axis, andthe Z-axis in the Z-axis; and perpendicularity errors between theX-axis, the Y-axis, and the Z-axis; calculating, based on the measuredactual error data errors with respect to the arbitrary coordinateposition in the machine tool coordinate system, following errors in athree-dimensional space of a set coordinate system having its origin ata reference position X_(a), Y_(a), Z_(a) preset in the machine toolcoordinate system: a positioning error in the X-axis direction in theX-axis feed mechanism; a positioning error in the Y-axis direction inthe Y-axis feed mechanism; a positioning error in the Z-axis directionin the Z-axis feed mechanism; translational errors in the X-axis feedmechanism, the Y-axis feed mechanism, and the Z-axis feed mechanism;angular errors around the X-axis, the Y-axis, and the Z-axis in theX-axis feed mechanism; angular errors around the X-axis, the Y-axis, andthe Z-axis in the Y-axis feed mechanism; angular errors around theX-axis, the Y-axis, and the Z-axis in the Z-axis feed mechanism; andperpendicularity errors between the X-axis, the Y-axis, and the Z-axis;and calculating, based on the calculated errors in the three-dimensionalspace of the set coordinate system, the relative motion error betweenthe spindle and the table in the three-dimensional space of the setcoordinate system.
 2. The method according to claim 1, whereinmeasurement of the perpendicularity errors between the X-axis, theY-axis, and the Z-axis is performed with a double ball bar.
 3. Themethod according to claim 2, wherein the calculated errors in thethree-dimensional space of the set coordinate system relates to aspindle center position on a front end of the spindle.
 4. The methodaccording to claim 2, wherein the relative motion error between thespindle and the table in the three-dimensional space of the setcoordinate system relates to a tip of a tool to be attached to thespindle.
 5. The method according to claim 3, wherein the relative motionerror between the spindle and the table in the three-dimensional spaceof the set coordinate system relates to a tip of a tool to be attachedto the spindle.
 6. The method according to claim 1, wherein thecalculated errors in the three-dimensional space of the set coordinatesystem relates to a spindle center position on a front end of thespindle.
 7. The method according to claim 6, wherein the relative motionerror between the spindle and the table in the three-dimensional spaceof the set coordinate system relates to a tip of a tool to be attachedto the spindle.
 8. The method according to claim 1, wherein the relativemotion error between the spindle and the table in the three-dimensionalspace of the set coordinate system relates to a tip of a tool to beattached to the spindle.